A cross cutter is known in the art from German Utility Model DE-GM 89 00 516, wherein pipe-shaped cutter cylinders formed of a composite carbon fiber material are rotatably seated in pairs above each other in a machine frame. The cutter holders fastened on each cutter cylinder, along with the cutters and the oppositely located counterweight, are still made of metal. In this case it is disadvantageous that the mass inertia moment of the rotating cutter cylinder system does not allow the highest operational rpm with reduced energy absorption. Furthermore, such a cross cutter does not produce the optimum cutting quality for the web because of the flexing of the cutter cylinders during cutting.